The short answer
Choose a group tour when you want a defined route and are comfortable sharing transport and guide time. Choose a private tour when your dates, pace, mobility needs or family routine require adjustments. Most importantly, ask what is actually private: the vehicle, the guide, the whole itinerary or only one excursion.
When a group tour works well
Shared tours are practical for classic day trips such as the Sacred Valley, Maras and Moray, Humantay Lake or Rainbow Mountain. The route, departure window and inclusions are usually defined in advance. This makes planning straightforward, but the group needs to follow the agreed schedule and meeting points.
When private is worth discussing
Private service makes more sense for families with young children, travelers who want more time at a site, groups with different fitness levels or itineraries connecting several regions. It can also help when you need a specific hotel pickup, a slower first day in Cusco or a route coordinated with trains and flights.
What to ask before booking
Ask who provides the transport, how many travelers share it, whether entrance tickets are included, where the guide joins the route and what happens if your train or flight changes. A clear answer is more useful than the label private or shared by itself.
Plan the right service for each day
You do not have to choose one format for the entire trip. Many travelers use a shared day trip for one excursion and private coordination for Machu Picchu, airport transfers or a multi-day route. Message Deicy with your group size and preferred pace, and she can recommend where flexibility matters most.